{
  "id": "math/0609304",
  "version": "v2",
  "published": "2006-09-11T18:59:00.000Z",
  "updated": "2007-11-13T21:32:40.000Z",
  "title": "String topology for spheres",
  "authors": [
    "Luc Menichi",
    "Gerald Gaudens"
  ],
  "comment": "22 pages. Minor corrections. An appendix by Gerald Gaudens and Luc Menichi has been added. Final version. To appear in Comment. Math. Helv",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "Let $M$ be a compact oriented $d$-dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin-Vilkovisky algebra on $\\mathbb{H}_*(LM)$. Extending work of Cohen, Jones and Yan, we compute this Batalin-Vilkovisky algebra structure when $M$ is a sphere $S^d$, $d\\geq 1$. In particular, we show that $\\mathbb{H}_*(LS^2;\\mathbb{F}_2)$ and the Hochschild cohomology $HH^{*}(H^*(S^2);H^*(S^2))$ are surprisingly not isomorphic as Batalin-Vilkovisky algebras, although we prove that, as expected, the underlying Gerstenhaber algebras are isomorphic. The proof requires the knowledge of the Batalin-Vilkovisky algebra $H_*(\\Omega^2 S^3;\\mathbb{F}_2)$ that we compute in the Appendix.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-13T21:32:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "string topology",
      "dimensional smooth manifold",
      "batalin-vilkovisky algebra structure",
      "hochschild cohomology",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9304M"
    }
  }
}